Describe the possible echelon forms of the following matrix. A is a 3 x 3 matrix...
i need help with these two questions. it is from linear algebra Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns. Select all that apply. (Note that leading entries marked with an X may have any nonzero value and starred entries may have any value including zero.) A. Х * B. 0 X 0 0 0 X C. х * D. 0 0 0 0 0 1 5 4 -5 -8...
is onto is o Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R Give some examples of the echelon forms. The leading entries, denoted , may have any nonzero value; the starred entries, denoted , may have any value (including zero). Select all that apply C. 0 0 0 0 B. A. E. 0 G. 0 is onto is o Describe the possible echelon forms of the standard matrix for a linear...
8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R
(1) A is a 3 x 7 matrix, in reduced echelon form, such that the general solution of the equation where t1, t2, t3, t4 are any real numbers. (a) Which variables are free variables? How can you tell? (b) Write down A. Is it possible to come up with multiple answers for this? (c) Are the vectors that are multiplied by t,tg,ts, t4 linearly independent? You can answer this question without doing any calculations. (1) A is a 3...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
List all or the possible echelon forms or the standard matri for a linear transformation : 3 → that is one to one. Use for pivot positions for en nes that may have any value and must be 0. Enter the matrices as a list separated by commas. Here is an example of the form that the answer should be in; this answer is very incorrect though: II.[0,01] for entries that entered as [IP,o1.[P.ll List all or the possible echelon...
Suppose the following matrix B is the echelon form of a matrix A: B = Answer the following questions with reasons. The word “plane” is being used below to mean planes of any dimension. (b) Before you knew B, how many planes in which dimensional space were intersecting to give the solution space of Ax = 0? (c) Looking at B, how many planes do you minimally need to cut out the solution space of Ax = 0? (d) Write...
Determine if the columns of the matrix form a linearly independent set. 1 2 - 3 8 12 37 -6 38 - 1 -8 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of [ A o]is | The columns are linearly independent because the reduced row echelon form of [ A 0 ] is B.
Determine if the columns of the matrix form a linearly independent set. 1 2-3 1 2 5 - 4 -2 - 14 2 7 2 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of is A 0 B. The columns are linearly independent because the reduced row echelon form ofA 0 is